Santos, who won the Nobel Peace Prize this month, said the government remained committed to making peace but would not budge from its demand for the ELN to first release former congressman Odin Sanchez.
"The formal installation of the negotiating table with (the ELN) is postponed until they release Odin Sanchez safe and sound," Santos said in a speech.
He said he had ordered the government's negotiating team to "suspend" its trip to the Ecuadoran capital Quito, where the talks had been due to formally open at 5:00 pm (2200 GMT).
The National Liberation Army (ELN) is Colombia's second-largest rebel group after the Revolutionary Armed Forces of Colombia (FARC), which has been in talks with the government for nearly four years.
The ELN talks are meant to open a new, decisive front in Santos's efforts to end an armed conflict that has lasted more than half a century and killed more than 260,000 people.
Santos has already signed a peace deal with the FARC, but voters rejected it in a referendum this month - sending negotiators back to the drawing board.
The ELN had promised to free its hostages before the talks - as the FARC did before starting negotiations in Cuba in 2012.
But it bristled last week when the government's chief negotiator, Juan Camilo Restrepo, gave it an ultimatum to free Sanchez. The ELN accused Restrepo of "torpedoing" the talks.
Since then, there has been no news on the fate of the hostage - or hostages, according to some sources - still being held by the leftist guerrillas.
Sanchez voluntarily went into ELN custody in April to take the place of his brother Patrocinio, a former governor who had fallen ill after three years in captivity.
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